(1) Repeal of all Naturalization Laws.
(2) None but Americans for office.
(3) A pure American Common School system.
(4) War to the hilt, on political Romanism.
(5) Opposition to the formation of Military Companies, composed of Foreigners.
(6) The advocacy of a sound, healthy and safe Nationality.
(7) Hostility to all Papal influences, when brought to bear against the Republic.
(8) American Constitutions & American sentiments.
(9) More stringent & effective Emigration Laws.
(10) The amplest protection to Protestant Interests.
(11) The doctrines of the revered Washington.
(12) The sending back of all foreign paupers.
(13) Formation of societies to protect American interests.
(14) Eternal enmity to all those who attempt to carry out the principles of a foreign Church or State.
(15) Our Country, our whole Country, and nothing but our Country.
(16) Finally,-American Laws, and American legislation; and death to all foreign influences, whether in high places or low!

Full document quoted by Sen. William Seward in debate over the Homestead Bill of 1850, himself being quoted in Republican Landmarks: The Views and Opinions of American Statesmen on Foreign Immigration by John P. Sanderson. (J.B. Lippincott & Co., Philadelpha: 1856) [Link]

It is unclear whether this document was formally passed as the official platform of the American Party in 1856 or is merely a common statement of principles shared widely among the party's membership.